Treffer: Generating MCMC proposals by randomly rotating the regular simplex

Title:
Generating MCMC proposals by randomly rotating the regular simplex
Authors:
Andrew J. Holbrook
Source:
J Multivar Anal
Publication Status:
Preprint
Publisher Information:
Elsevier BV, 2023.
Publication Year:
2023
Subject Terms:
Haar measure, FOS: Computer and information sciences, Other Statistics (stat.OT), Monte Carlo methods, 02 engineering and technology, parallel MCMC, Statistics - Computation, 01 natural sciences, Article, Markov chain Monte Carlo, Statistics - Other Statistics, 0202 electrical engineering, electronic engineering, information engineering, Numerical analysis or methods applied to Markov chains, 0101 mathematics, Computational methods for problems pertaining to statistics, Computation (stat.CO), orthogonal group
Document Type:
Fachzeitschrift Article<br />Other literature type
File Description:
application/xml
Language:
English
ISSN:
0047-259X
DOI:
10.1016/j.jmva.2022.105106
DOI:
10.48550/arxiv.2110.06445
Access URL:
https://pubmed.ncbi.nlm.nih.gov/37799825
http://arxiv.org/abs/2110.06445
https://zbmath.org/7636963
https://doi.org/10.1016/j.jmva.2022.105106
Rights:
CC BY NC ND
arXiv Non-Exclusive Distribution
URL: http://creativecommons.org/licenses/by-nc-nd/4.0/This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/ (http://creativecommons.org/licenses/by-nc-nd/4.0/) ).
Accession Number:
edsair.doi.dedup.....91e87183e77bd2cb0ed4ceb9d585d7c7
Database:
OpenAIRE

Weitere Informationen

We present the simplicial sampler, a class of parallel MCMC methods that generate and choose from multiple proposals at each iteration. The algorithm's multiproposal randomly rotates a simplex connected to the current Markov chain state in a way that inherently preserves symmetry between proposals. As a result, the simplicial sampler leads to a simplified acceptance step: it simply chooses from among the simplex nodes with probability proportional to their target density values. We also investigate a multivariate Gaussian-based symmetric multiproposal mechanism and prove that it also enjoys the same simplified acceptance step. This insight leads to significant theoretical and practical speedups. While both algorithms enjoy natural parallelizability, we show that conventional implementations are sufficient to confer efficiency gains across an array of dimensions and a number of target distributions.
To appear in Journal of Multivariate Analysis. Code here: https://github.com/andrewjholbrook/simplicialSampler